515
A Comparison of Carbon Monoxide and Nitrogen as Ligands in Transition Metal Complexes Kenneth G. Caulton, Roger L. DeKock, and Richard F. Fenskel
Contribution from the Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706. Received June 26, 1969 Abstract: The bonding characteristics of CO and Nz in transition metal complexes are investigated on the basis of comparative molecular orbital calculations for Cr(CO), and Cr(NJ8. The results suggest that the differences in ir acceptor ability of the N, ligand compared to CO are consequences of the off-diagonal matrix element between the metal d orbitals and the ir antibonding orbital of the ligand moieties. The Q bonding interactions can be mainly characterized as electron donation to the metal from orbitals substantially localized on the atoms adjacent to the metal. However, these orbitals have sufficient u antibonding properties with respect to the ligand u bond character that some degree of “within ligand” Q bond strengthening on complex formation cannot be ruled out. The results suggest that some of the apparent conflicts in ir acceptor ability of the two ligands may be attributed to combined u-ir factors.
T
here has been a recent surge of interest in the synthesis and study of transitionmetal complexes of molecular nitrogen. 2-7 Nitrogen was long thought to have no affinity for transition metals on the basis of the inertness of gaseous nitrogen itself, but it now seems that it was merely necessary to develop a sufficiently clever synthetic route to nitrogen complexes. Along with the progress in synthetic routes to these complexes there has developed some disagreement as to the ir acceptor ability of N2 relative to CO. Thus, claim on the basis of relative changes in Collman, et N2 and CO stretching frequencies in analogous compounds that “Nz is a more powerful i~ acid than CO.” In the same paper they also state that “Nitrogen is similar to NO+ inasmuch as both are strong ir acids and weak u donors.” Conversely, Bancroft, et u Z . , ~ state as a consequence of Mossbauer studies that ‘ T O is an appreciably better u donor and/or T acceptor than Nz.” From a theoretical standpoint, CO and Nz are interesting ligand species. As free molecules, the calculated orbital energies of the two species* are surprisingly similar if one considers that the transfer of a proton from one nucleus to the other is involved in comparing the two isoelectronic molecules. Since Nzforms complexes which are structurally sirnilarg~’O to those of CO, a comparison of the electronic structures of analogous complexes of CO and Nz would be enlightening. Unfortunately the other ligands contained in known analogous species are of such complexity and the species are of such low molecular symmetry that theoretical computations are impossible without making severe simplifications in the calculations. Consequently, it was decided to undertake comparative calculations on the well-known compound, Cr(C0)6, and the hypothetical (1) Author to whom reprint requests should be directed. (2) A. D . Allen and C. V. Senoff, Chem. Commun., 621 (1965). (3) J. P. Collman and J. W. Kang, J . Amer. Chem. Soc., 88, 3459 (1 9 66). (4) J. E. Fergusson and J. L. Love, Chem. Commun., 399 (1969). ( 5 ) J. P. Collman, M. Kubota, F. D. Vastine, J. Y . Sun, and J. W. Kang, J . Amer. Chem. Soc., 90, 5430 (1968). (6) G. M. Bancroft, M. J. Mays, and B. E. Prater, Chem. Commun., 5 8 5 (1969). (7) G. Speier and L. Marko, Inorg. Chim. Acta, 3, 126 (1969). (8) B. J. Ransil, Reu. Mod. Phys., 32, 245 (1960). (9) J. H. Enemark, B. R . Davis, J . A. McGinnety, and J. A. Ibers, Chem. Commun., 96 (1968). (10) F. Bottomley and S. C . Nyburg, ibid., 897 (1966).
molecule, Cr(N&. Not only does the high symmetry of this latter species make the calculations more tractable, but it permits one to focus attention on the bonding properties of NP relative to CO without the complexities introduced by the presence of other ligand species.
Calculational Method Since the publication of the earlier results from this laboratory l 1 for Cr(CO)6, minor changes have been made in the computational method in order to simplify the calculational procedure. For example, recent investigations l 2 have indicated that the three-center nuclear attraction integral can be very well approximated by
where S(q5,, xb) is the overlap integral of the functions on centers a and b; qv is the charge on center v, R,, and Rbv are the internuclear distances between the a and v centers and b and v centers, respectively. The basis functions and internuclear distances for Cr(CO)6 were the same as those used previously. For purposes of comparison, the eigenvalues of the occupied orbitals obtained previously and in the present work are listed in Table I. The interpretations presented in our earlier communication1’ are completely unaffected by the small deviations in the eigenvalues listed in the table. As would be expected in the case of such close agreement, the eigenfunctions of the two sets of calculations are very similar as well. In accord with the X-ray structural analysis’O of Ru(NH&NZ2+ which shows that the Nz ligand bonds end-on through only one nitrogen, the calculations on the hypothetical Cr(N& assumed a structure analogous to Cr(CO)6. The chromium-cacbon distance was set at the known distance of 1.92 A.13 The Shromiumnitrogen distance was also taken as 1.92 A so that a comparison of CO and Nz as ligands would be unfettered by bond length changes. This invariance of Cr-N and Cr-C bond lengths is not incompatible with (11) I(. G. Caulton and R. F. Fenske, Inorg. Chem., 7 , 1273 (1968). (12) (a) I. H. Hillier, J . Chem. SOC.,A , 878 (1969); (b) R. L. De Kock, Ph.D. Thesis, University of Wisconsin, 1970. (13) A. Whitaker and J . W. Jeffery, Acta Crystallogr., 23, 977 (1967).
Caulton, DeKock, Fenske
Comparison of CO and Nz as Ligands
516 Table I. Eigenvalues of Occupied Orbitals of Cr(C0)s and Cr(Nz)ea
Orbital
a
In eV.
Cr(COh, previous workb
Cr(COh, present work
Cr(Nz)e, present work
-37.22 -18.51 -15.23 -37.33 -19.01 -16.14 -37.21 -17.69 -14.97 -14.02 -14.95 -14.90 -16.24 -8.19
-38.00 -18.78 -17.28 -38.79 -19.37 -17.42 -38.14 -17.35 -16.87 -15.24 -15.39 -15.36 -15.80 -8.30
-37.33 -21.31 -17.46 -38.23 -23.14 -17.51 -37.39 -20.84 -17.47 -16.75 -16.83 -16.86 -17.10 -7.60
orbital basis set used to carry out the calculations. The presentation of the eigenvectors in terms of ligand MO participation will aid in the discussion of the bonding characteristics of the species. Even a cursory examination of the eigenvalues of Cr(CO), and Cr(N2), given in Table I suggests that the stability of the former cannot be deduced on the basis of orbital energies. While the stability of a compound requires the consideration of many factors, such as the stability of the separated moieties, it is nevertheless somewhat surprising that the eigenvalues in the two cases are so similar. It is informative to examine the stabilization of the metal 3dn orbitals as a consequence of interaction with the ligand l n and 2 n orbitals. Table IV summarizes the pertinent information. Notice that the quantity, E(2t2g)- F(3dn, 3dn), for Cr(CO), is -2.49 eV, while its value for Cr(N& is only - 1.18 eV. Whether or not the
Reference 11.
Table 11. Eigenvectors and Eigenvalues of Occupied Orbitals of CO and Nza CO
2sC
2puc
2so
2puo
3ud 4u 5u
0.285 0.223 0.785
0.237 0.169 -0.617
0.698 -0.485 -0.070
0.101 0.813 -0.144
2paC
lA
27re Nz
2sN1
2ugd 2uu 3r e 1A" 1A g e
0.495 0.589 0.370
2p~Ni 0.206 -0.398 -0.614
2sN2
2p~Nz
0.495 -0.589 0.370
0.206 0.398 -0.614
2p7ro
0.494 0.909
0.752 -0.711
2p~N1
2p?rNz
0.624 0.835
Eigenvalueb SCF eigenvalue" -38.60 -17.95 -14.63 -16.24 -1.32
-40.78 -19.93 -13.08 -15.86 7.09
Eigenvalueb SCF eigenvaluec -36.30 -17.42 -16.46 -16.09 1.71
0.624 -0,835
-39.52 -19.88 - 14.82 -15.77 7.43
b All eigenvalues are listed in units of eV. SCF results are taken a The coordinate systems are such that u overlap integrals are positive. from ref 8. d Our method treated the 1s functions as part of the core. The orbital designation used here is in accord with the SCF results which treat the 1s functions as part of the basis set. e The 2~ orbitals are unoccupied but are included here because of their significance in the bonding to the metal atom.
the X-ray diffraction results of Davis, Payne, and IbersI4 on C O ( N ~ ) H [ P ( C ~ H ~which ) ~ ] ~ showed , that the observed Co-N2 distance is similar to Co-CO distances in various cobalt carbonyl complexes. The nitrogen AO's and the nitrogen-nitrogen distance were the same as those used by R a n d 8 in his SCF calculation on Nz using the Slater basis set.
Results and Discussion Because they will be convenient for later discussion, the eigenvectors and eigenvalues of the free ligand species, CO and Nz, are given in Table 11. These results are in reasonable accord with rigorous SCF values,8 particularly when one considers the approximations involved in our calculational method. The results affirm the previously stated similarity in eigenvalues for the two species. The eigenvalues for Cr(CO), and Cr(N& are presented in Table I. Since our previous work1' tabulated the eigenvectors of Cr(CO),, which are essentially equivalent to those obtained in this work, only the Cr(NJ6 eigenvectors are tabulated in Table 111. As with Cr(CO),, the eigenvectors of Cr(N& are reported in terms of the free ligand basis functions, i.e., the functions listed in Table 11, rather than in terms of the atomic (14) B. R. Davis, N. C . Payne, and J. A. Ibers, J . Amer. Cham. Soc., 91, 1240 (1969).
Journal of the American Chemical Society
2tzglevel is higher or lower in energy than the diagonal matrix element, F(3dn, 3dn), depends upon the competition between the F(3dny I n ) and F(3da, 2n) interactions. In Cr(CO)B, these are -4.34 and -7.36 eV, respectively. However, the corresponding terms in Cr(N& are - 4.76 and - 5.77 eV. The reason for the reduction of F(3dx, 2n) in the case of the nitrogen complex is apparent upon consideration of the form of the 2n ligand wavefunction and the resultant matrix element. A general form of the function is WK)
= Cl4l
- cs4z
(2)
in which the negative sign is consequence of the antibonding character of the function (see Table 11); 41 is a normalized symmetry adapted linear combination c?f wave functions on those atoms adjacent to the chromium atom, and is a similar set of functions on the more distant atoms. Expressed in this way, the coefficients, c1 and cn, can be taken directly from Table TI. The matrix element then has the form F ( 3 d ~ 2n) ,
=
Cl(3dTjFI41) - ~2(3d~1F/4z)(3)
Because of the greater proximity of atom one to the metal atom, (3dn(F'~$~) will be larger than (3dx'F~&) in both ligands. In free Nz,the two coefficients, c1 and czyare identical and the total matrix element re-
/ 92:3 / February 11, 1970
517 Table In. Eigenvectors of Occupied Orbitals of Cr(Nz)s in a Basis of Free N2 MO's 3u
4u
5u
lal, 2al, 3alg
1.0097 -0.0821 -0.0042
0.0234 0.5828 -0.6808
0.0102 0.4585 0.7539
1% 2% 3%
3u 1.0643 - 0.0613 -0.0005
4u 0.0321 0.5117 -0.6961
ltrg 2t2,
la 0.9757 -0.3386
Itl" 2tl" 3ti~ 4tiu
4s
0.0015 0.0201 0.0054
-0.0552 0.2993 0.0535
0.4962 0.6968
60. -0.0056 0.0117 -0.0046
3du -0.0108 0.3855 0.0162
4du -0.1648 0.1393 0.0338
2a 0.0592 0.4774
3da 0.1519 0.7809
4da -0.0634 0.0635
30 1.0272 -0.0660 -0.0050 0,0032
40 0.0214 0.6032 -0.6720 -0.0182
5u
6u -0.0019 0.0147 0. 0052 -0.0020
la
0.0047 0.5019 0.7385 0.0497
2a -0.0037 -0.0075 -0.0036 0.0376
17 0.9993
2a 0.0426 0.0417
ltzu ltl,
1.oooO
Table IV. Tzg Representation: and Eigenvalues
3da
F Matrix for Cr(CO), -15.34 -1.22 -4.34 -2.34 -7.36 -5.81
+
5u
o.ooo1
Matrices," 2t2, Eigenfunctions, 2a
la l?r 2a 3da 4dr
60
+
il/(2tzg) = -0.34(1~) 0.54(2~) 0.69(3dn) E(%,) = -8.30eV F Matrix for Cr(Nz)s la -16.71 -0.99 -4.76 2a -0.76 -5.77 3d* -6.42 4da
4da
-0.0095 0.0417 -0.0154 1.0038
+ 0.04(4da)
0.3139 0.0502 0.0221
Table V. Contributions to F(3da, 2a) in the Tz,Representation
CI
cz
-3.05 -5.48 0.00 10.09
4P
- 0.0843
(3daIFl$Jl), eV (3dn~F;+z),eV F(3dr, 2a), eV
co
Nz
0.909 0.711" -8.27 -0.22 -7.36
0.835 0.839 -7.20 -0.31 -5.77
The sign in front of cz was changed from that listed in Table I1 to conform to eq 3.
of the diagonal matrix elements. In this work, the difference in 27r interaction appears to be equally a function of the decreased value of the off-diagonal matrix element. iC.!ftzg) = -0.34117) -t0.48(2*) + 0.78(3da) + 0.0q4da) Parenthetically, it might be noted that while the E(2t2,) = - 7.60 eV method employed here results in a stabilization of the 2t2g level, in accord with long held qualitative argua In units of eV. ments, l7 more simplified calculational techniques such as the well-known SCCC method of Gray and coflects the diflerence between (3dn1Fiq51) and (3d~IFi+~). workers, l8 which employ the Wolfsberg-Helmholz Since hT2 and CO are isoelectronic, the differmethod for evaluation of F(3d7r, 17 r ) and F(3d7r, 27r) alence in the two molecules lies in the transfer of a proton ways appear to result in a destabilization of the level. from atom 1 to atom 2 . Hence +1 on the carbon atom This result occurs because the off-diagonal elements are should be more diffuse while +%on the oxygen becomes estimated by more contracted, which should increase the magnitude F ( 3 d ~ IT) , = K.G(3di~,l ~ ) [ F ( 3 d 3~ d, ~ ) of (3d7rIF1+J and decrease ( 3 d ~ 1 F l 4 ~in) CO compared to Nz. Furthermore, in CO the c1 coefficient is W w , 17r)1/2 (4a) larger than cz, 0.91 compared to 0.84. Both effects inand crease the first and decrease the second term in eq 3, F(3dw, 2 ~ =) K.G(3dr, 2~)[F(3dw,3 d ~ ) which results in a substantial increase in the value of the total matrix element for CO. These qualitative arguW w , 2w)1/2 (4b) ments have also been considered by Jaffd and Orchin'S where G(i, j) is the group overlap integral, K is a factor and are now confirmed by the values given in Table V. (sometimes a function of G(i, j) ) often set equal to 2.0. The decreased 3d7r-27r interaction coupled with the The values used for F(lw, I n ) are so much greater than greater separation of the 3dw and 2w diagonal matrix those used for F(2s, 27r) that the matrix element F elements accounts for the decreased 2w and increased (3dw, 1 ~ is ) substantially larger than F(3dw, 27r), 3da character in the 2tZgmolecular orbital for the Crcausing the destabilization. Such a result appears to be (N2)R species. In the results" on the isoelectronic series, V(CO)6-, (16) L. E. Orgel, "An Introduction to Transition Metal Chemistry," 2nd ed, Methuen and Co., Ltd., London, 1966, p 138. Cr(CO)6, and MII(CO)~+,it was noted that the de(17) F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemiscreasing 2w participation in the 2tZgmolecular orbital try," 2nd ed, Interscience Publishers, New York, N. Y., 1966, p 707. was primarily a consequence of an increasing separation (18) (a) J. J. Alexander and H. B. Gray, Coord. Chem. Rev., 2, 29 -4.09 -5.57 0.00 9.42
+ +
(15) H. H. Jaffe and M. Orchin, Tetrahedron, 10, 212 (1960).
(1967); (b) J . Amer. Chem. SOC.,90,4260 (1968); (c) N. A. Beach and H. B. Gray, ibid., 90, 5713 (1968).
Caulton, DeKock, Fenske J Comparison of CO and NZas ligands
518 Table VI. Electron Distribution in Cr(COh and Cr(N& Cr(CO)e 3.57 1.50 Cr(Nz)6 4.12 1.07 For Cr(N2)e: e4 = (1/
